Research On The Valuation Of Convertible Bonds Of Listed Companies In China

Convertible bonds appear in China security market for few years, and which have become an important type of financing instrument. It is of great significance to evaluate convertible bonds for issuing companies designing issuance provisions, investors reasoningly investing, and convertible bonds market developing healthily. This paper studies the valuation of convertible bonds, by making use of modern financial mathematics, financial engineering, partial derivative function and finite element method. There are three valuation models deduced based on the contingent claims analysis. The first one is the single factor model, in which convertible bond is regarded as the derivative of underlying stock. The second model takes the credit risk into account based on the intensity model, in which the credit risk of convertible bonds decreases along with the underlying stock price's declining, and increases along with underlying stock price's climbing, it is because of the issuing company is more likely to default with lower stock price. Thirdly a dual factors model is deduced, which integrate the interest rate risk and market risk. The stochastic interest rate is characterized as the Hull-White model, which has an advantage of fixing the current term structure exactly. Convertible bonds possess early conversion provision, callability provision and putability provision. Those provisions all have American feature, so the valuation of convertible bonds is corresponding to a free boundary problem. By establishing variational inequality, Finite element (FE) method is applied to solved those valuation models, which has some clear advantages over finite difference method: FE can deal with any solution domain; FE provide accurate Greeks (risk management parameters) as a by-product; and FE provide more flexibility in terms of incorporating final conditions and handling boundary conditions. After research on the callability protection terms of convertible bonds of China market, it is founded that all of the convertible bonds have strong callability protection terms, which is compared with the result of oversea market. A quantitative research on the effect of callability provision and putability provision to the convertible bonds value is carried out, by calculating the convertible bonds under different provisions, and it is discovered that the callability price and putability price is the most sensitive factor for the effect. An investigation of the pricing of 19 convertible bonds on the China convertible bond market using daily market prices for a period from the corresponding listed date to 12 Dec. 2003 is implemented. And there is a underpricing of 11.66% exists on average, i.e., market prices are 11.66% below model prices. The reasons of the underpricing include: the low liquidity of convertible bonds, which restricts the price-founding function of the market, and the lack of short-sell, which can achieve free arbitrage if the market prices departure the equilibrium prices.